Define the limiting current in a fuel cell or electrode reaction and give a simple expression.

• A. i_L = n F A D C / δ
• B. i_L = δ / (n F A D C)
• C. i_L = n F A / (D C δ)
• D. i_L = n F A D C δ

Answer: (A)

Limiting current is the diffusion-limited current: the rate at which the reacting species can reach the electrode by mass transport sets the pace of the reaction, not the surface kinetics. For a simple planar diffusion layer of thickness δ, the steady-state diffusive flux to the electrode is J = D(C_bulk − C_surface)/δ. In the limiting case the surface concentration is essentially zero because the species is consumed as fast as it arrives, so J ≈ DC/δ. The current is i = nFAJ, giving i_L = nFAD C / δ. This shows i_L increases with diffusion coefficient D, bulk concentration C, electrode area A, and number of electrons n, and decreases with diffusion-layer thickness δ. The other expressions place δ in the wrong position or have the wrong dependence, which would not reflect the diffusion-limited nature of the process.